A rigid, not infinitesimally rigid surface with K ample

We produce an example of a rigid, but not infinitesimally rigid smooth compact complex surface with ample canonical bundle using results about arrangements of lines inspired by work of Hirzebruch, Kapovich & Millson, Manetti and Vakil.

Tunable adhesion of an elastic pillar by pressurizing inner cavity

This work studies the effect of a cavity with inner pressure on the adhesion of circular pillars with a flat tip in contact with a rigid smooth surface. The inner cavity of pillars is pressurized positively before the contact. The effect of the cavity on the adhesion is examined for different cavity diameters and different membrane thicknesses over the cavity. The shape of the tip of the pillars is changed in accordance with the cavity dimension and the positive cavity pressure, which allows the change of an adhesive contact type from a flat-punch adhesive contact to a spherical adhesive contact that results in tunable adhesion strength of circular pillars. The results demonstrate that having an inner cavity reduces the adhesion, where the cavity diameter is more effective than the membrane thickness over the cavity on the reduction of the adhesive force. Applying pressure to the inner cavity of the pillars changes the sphericity, which alters the adhesive force accordingly. The sphericity 0.1 almost has no effect on the tunable adhesion strength, where the higher sphericity results in the reduction of the adhesive force from high adhesive force to low adhesive force linearly with a tunable efficiency between 95% and 98%.

Theoretical model of the effect of dimple on friction behavior in hydrodynamic lubrication regime

In this paper, full-film lubrication between the rigid smooth and dimpled surfaces was addressed. A theoretical model is developed to study the effect of a dimple on friction where the smooth surface is rotating while the dimpled surface is at rest. To simplify the problem, the magnified dimple cell is investigated along with some assumptions. Because dimples deploy periodically along with the x and y directions, the lubricant pressure also deploys periodically. A theoretical model can be developed for one cell and then extended to the whole surface. The main goal of this study is to understand the dimple effect on friction in a hydrodynamic lubrication regime. The main applications of this model are several types of bearings (point contact, line contact etc.) and mechanical parts where two surfaces interact in relative motion. Findings the optimum dimensions for the dimples also seem to be one of the interesting research areas in mechanization of agricultural and renewable energy sources.

Air mediates the impact of a compliant hemisphere on a rigid smooth surface

When a soft elastic body impacts upon a smooth solid surface, the intervening air fails to drain, deforming the impactor. High-speed imaging with the VFT reveal rich dynamics and sensitivity to the impactor's elastic properties and the impact velocity.

Investigation of running-in process based on surface roughness parameters, real contact area ratio and tribological properties

The running-in process is the initial process for the new moving parts wearing against each other to establish the shape adjustment that will regulate them into a stable relationship for the rest of their working life. The objective of this research is to investigate and evaluate the running-in process by using disk-on-block line contact device. Due to its empirical nature and well-ploughed analysis, an asperity micro-contact model is considered. The experiment is performed by varying the surface roughness of the block with rigid smooth sphere surface under specific condition. The effects of surface roughness, load, speed, and lubrication on the running-in behaviour is studied. The running-in process encourage plastic deformation of asperities and created microstructural changes on contact surfaces. The theoretical and experiment result shows that the plasticity index ps, surface roughness parameter b, real contact area ratio * A0 and specific film thickness l is influenced by the running-in process.

Influences of Morphology Parameters on the Contact Behavior of a Steel Interface

The surface roughness induced by geometric irregularities (asperities) has substantial influence on the contact stiffness, which further affects the working performance and service life of mechanical equipment. In this study, an elastic–plastic contact law between a sinusoidal asperity and a rigid smooth flat is first studied, which is then applied on a statistical model to simulate the contact behavior of a pair of 18CrMo4 steel surfaces to investigate the influences of morphology parameters on the contact stiffness. The analysis shows that smaller shape ratios [Formula: see text] and larger wavelengths [Formula: see text] induce larger normal contact stiffness [Formula: see text] for surfaces with identical roughness, wherein the roughness is defined by the mean value of asperity heights [Formula: see text] and the standard deviation of asperity heights [Formula: see text]. The normal contact stiffness increases as [Formula: see text] decreases under the same loading conditions, while the normal contact stiffness increases as [Formula: see text] decreases for surfaces with a fixed [Formula: see text]. Besides, the normal pressure and normal contact stiffness derived from the proposed contact model are validated. The results demonstrate the potential of the proposed model in contact design due to its ability of establishing the relations between the normal contact stiffness and surface morphology parameters.

Indentation and flattening of rough surfaces spherical asperities

The paper indicates that the application of roughness models and the theories of contacting rough surfaces developed by Greenwood-Williamson and N.B. Demkin for solving the problems of hermetology leads to significant errors. This is explained by much greater contact pressures than for the tribology problems, by describing only the initial part of the reference surface curve, the lack of allowance for the plastic extrusion of the material. A brief review of methods for describing the introduction of a sphere into an elastoplastic reinforced half-space is given. The properties of the elastoplastic reinforced material are described by the power law of Hollomon. To describe the indentation and flattening of single spherical asperity, the results of finite element modeling are used. The cases of contacting a rigid rough surface with an elastoplastic half-space and a rigid smooth surface with a rough surface are considered. To determine the relative contact area, the discrete roughness model is used in the form of a set of spherical segments distributed along the height in accordance with the curve of the reference surface.

Wall pressure coherence in supersonic turbulent boundary layers

A numerical database (Bernardini & Pirozzoli, Phys. Fluids, vol. 23, 2011, 085102) is analysed to investigate cross-statistics of wall-pressure fluctuations induced by supersonic turbulent boundary layers developing over a rigid smooth wall without a pressure gradient. The Mach number spans from 2 to 4 and a relatively large range of Reynolds numbers is considered. It is shown, for the first time, that the cross-statistics of wall-pressure fluctuations at such high Mach numbers is very similar to that usually observed in incompressible flow conditions. Furthermore, it is demonstrated that theoretical predictions provided by the well-known Corcos and Efimtsov models continue to apply.

Theory and Practice of Technology for Machining Non-Rigid Smooth Shafts

In modern machine-building the problem of creating highly-efficient technological mechanical machining processes, taking into account the energy and resources-saving and ecological requirements is one of the paramount importance. Throughout the whole period of machine-building technology development there were great difficulties owing to the problems of machining parts with low rigidity and high demands on quality. At creating the technological processes of similar parts’ machining, as at creating any technological process, it is necessary to provide realization of the principle of combining technical, economic and organization assignments. But unlike usual technological processes, in this case it is much more difficult to meet all these requirements.